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Lapatulllka [165]
2 years ago
9

Solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 ​

Mathematics
1 answer:
ratelena [41]2 years ago
4 0

Answer:

Solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 ​we get x=2 and y=-3

Solution set = {2,-3}

Step-by-step explanation:

We need to solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 ​

let:

3x-2y=12--eq(1)\\x+3y=-7 --eq(2)

Finding value of x from equation 2 and putting in eq(1)

From \ eq(2)\\x+3y=-7\\x=-7-3y

Putting value of x in eq(1)

3x-2y=12\\Put \ x=-7-3y\\3(-7-3y)-2y=12\\Solving\\-21-9y-2y=12\\-11y=12+21\\-11y=33\\y=\frac{33}{-11}\\y=-3

So, we get y=-3

Now put value of y in equation 2 to find value of x

x+3y=-7\\x+3(-3)=-7\\x-9=-7\\x=-7+9\\x=2

So, we get value of x =2

So, solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 ​we get x=2 and y=-3

Solution set = {2,-3}

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Hector spent $41.75 for 2 DVDs that cost the same amount. The sales tax on his purchase was $3.15. Hector also used a coupon for
kykrilka [37]

Given:

Amount spent on 2 DVDs = $41.75

Sales tax = $3.15

Coupon = $1.00 off

To find:

The cost of each DVD.

Solution:

Let x be the cost of each DVD.

Then, cost of two DVDs = 2x

Amount spent of 2 DVDs = Cost of 2 DVDs + Sales tax - Coupon discount

41.75=2x+3.15-1.00

41.75=2x+2.15

41.75-2.15=2x

39.6=2x

Divide both sides by 2.

\dfrac{39.6}{2}=x

19.8=x

Therefore, the cost of each DVD is $19.8.

8 0
3 years ago
Can someone help me find the equivalent expressions to the picture below? I’m having trouble
miss Akunina [59]

Answer:

Options (1), (2), (3) and (7)

Step-by-step explanation:

Given expression is \frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}.

Now we will solve this expression with the help of law of exponents.

\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}=\frac{\sqrt[3]{(2^3)^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}

           =\frac{\sqrt[3]{2\times 3} }{3\times2^{\frac{1}{9}}}

           =\frac{2^{\frac{1}{3}}\times 3^{\frac{1}{3}}}{3\times 2^{\frac{1}{9}}}

           =2^{\frac{1}{3}}\times 3^{\frac{1}{3}}\times 2^{-\frac{1}{9}}\times 3^{-1}

           =2^{\frac{1}{3}-\frac{1}{9}}\times 3^{\frac{1}{3}-1}

           =2^{\frac{3-1}{9}}\times 3^{\frac{1-3}{3}}

           =2^{\frac{2}{9}}\times 3^{-\frac{2}{3} } [Option 2]

2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2 [Option 1]

2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2

                =(2^2)^{\frac{1}{9}}\times (3^2)^{-\frac{1}{3} }

                =\sqrt[9]{4}\times \sqrt[3]{\frac{1}{9} } [Option 3]

2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(2^2)^{\frac{1}{9}}\times (3^{-2})^{\frac{1}{3} }

               =\sqrt[9]{2^2}\times \sqrt[3]{3^{-2}} [Option 7]

Therefore, Options (1), (2), (3) and (7) are the correct options.

6 0
2 years ago
The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution. What amount of each solution do
xenn [34]

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

\texttt{ }

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

  • <em>Elimination Method</em>
  • <em>Substitution Method</em>
  • <em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

\texttt{ }

<em>Let:</em>

<em>Volumes of 2% Solution = x</em>

<em>Volumes of 10% Solution = y</em>

\texttt{ }

<em>Total Volume = 10 ml</em>

\boxed{x + y = 10} → <em>Equation 1</em>

\texttt{ }

<em>The nurse needs to mix 2% solution with 10% solution to get 10 ml of the prescribed 6% solution</em>.

2 \% x + 10 \% y = 6 \% (10)

2x + 10y = 6(10)

\boxed{x + 5y = 30} → <em>Equation 2</em>

\texttt{ }

<em>Equation 1 - Equation 2:</em>

( x + y ) - ( x + 5y ) = 10 - 30

-4y = -20

y = -20 \div -4

y = 5 \texttt{ ml}

\texttt{ }

x + y = 10

x + 5 = 10

x = 5 \texttt{ ml}

\texttt{ }

<h2>Conclusion:</h2>

<em>Volumes of 2% Solution = </em><em>5 ml</em>

<em>Volumes of 10% Solution = </em><em>5 ml</em>

\texttt{ }

<h3>Learn more</h3>
  • Perimeter of Rectangle : brainly.com/question/12826246
  • Elimination Method : brainly.com/question/11233927
  • Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

6 0
3 years ago
Plssss help fast and give a small explanation
Marrrta [24]

Answer: the area of the triangle is 23.4 cm²

Step-by-step explanation:

The given triangle is not a right angle triangle. Since two sides and one angle are known, we can either apply the Heron's formula or the Sine formula which is expressed as

Area of triangle = 1/2abSinC

Where a and b are the sides of the triangle and C is the given angle. Therefore,

Area = 1/2 × 8.2 × 6.4 × Sin63

Area = 1/2 × 8.2 × 6.4 × 0.8910

Area = 23.4 cm² to the nearest tenth.

6 0
3 years ago
Thanks for your answer
pogonyaev
I just had a test on this lol perfect timing. Anyways the answer would be 3 times bigger bc the circumference of a circle with the radius of 3 is 6pi and the circumference of a circle with the radius of 1 is 2pi which makes the first circle 3 times bigger
5 0
3 years ago
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